Lévy area for Gaussian processes: A double Wiener-Itô integral approach
Résumé
Let and be two independent continuous centered Gaussian processes with covariance functions and . We show that if the covariance functions are of finite -variation and -variation respectively and such that , then the Lévy area can be defined as a double Wiener-Itô integral with respect to an isonormal Gaussian process induced by and . Moreover, some properties of the characteristic function of that generalised Lévy area are studied.
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